An Analytic Theory on How Friction Affects Free Internal Waves in the Equatorial Waveguide

Abstract

We study theoretically the effects of linear (Rayleigh) friction on free internal waves in the equatorial wayeguide. The waves may be vertically propagating or in standing vertical modes. Analytic solutions on a beta-plane show that the meridional scale of the wayeguide becomes significantly larger than the inviscid value only when the frequency is much less than the friction coefficient. In the limit of zero frequency, the meridional scale grows without bound. The amount of zonal damping depends on the wave type. Kelvin, high-frequency Yanai (mixed Rossby-gravity), inertial-gravity and low-wavenumber (non-dispersive) Rossby waves decay relatively slowly while low-frequency Yanai and high-wavenumber (short) Rossby waves are much more strongly attenuated. With friction, transitions to evanescence are spread over frequency bands; waves that had zero group velocity without friction are zonally evanescent with friction. Off the equator, friction changes amplitude nodes into non-zero minima and smooths sharp phase shifts; phase lines slant backward relative to the direction of phase propagation. By symmetry, nodes and phase shifts of π are preserved on the equator. Friction alters the relative amplitudes and phases of the dynamic variables. When the frequency is much less than the friction coefficient, the motion obeys diffusion-dynamics rather than wave-dynamics.